x-ray spectroscopy workshop cambridge, ma matthew carpenter, ucb ssl 7/11/2007, comparison of...
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X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL 7/11/2007,
Comparison of Observed and Theoretical Fe L Emission from CIE Plasmas
Matthew CarpenterUC Berkeley Space Sciences Laboratory
Collaborators
Lawrence Livermore National Lab Electron Beam Ion Trap (EBIT) Team
P. Beiersdorfer
G. Brown
M. F. Gu
H. Chen
UC Berkeley Space Sciences Laboratory
J. G. Jernigan
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Overview
Introduction to the Photon Clean Method (PCM) An Example : XMM/RGS spectrum of Ab Dor PCM algorithm internals Analysis Modes: Phase I and Phase II solutions Bootstrap Methods of error analysis Summary
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Photon Clean Method: Principles
• Analysis uses individual photon events, not binned spectra• Fitting models to data is achieved through weighted random trial-and-error with feedback• Individual photons span parameter and model space, and are taken to be the parameters• Iteration until quantitative convergence based on a Kolmogorov-Smirnov (KS) test• Has analysis modes which allow divergence from strict adherence to model to estimate differences between model and observed data
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Photon Clean Method: Event-Mode Data and Model
Both data and model are in form of Event Lists (photon lists)
Monte-Carlo methods are used to generate simulated photons
Generation parameters for each photon are recorded
Each photon is treated as independent parameter
Single simulated photon:
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
PCM analyzes Simulated Detected sim or Esim
Observed Data(Event Form)
Simulated Data
Data representation inside program
Target: AB Dor (K1 IV-V), a young active star and XMM/RGS calibration target
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Target: AB Dor (K1 IV-V), a young active star and XMM/RGS calibration target
PCM analyzes Simulated Detected sim or Esim
The Photon Clean Method algorithm analyzes and outputs models as event lists *** All histograms in this talk are for visualization only
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
PCM analyzes Simulated Detected sim or Esim
Target: AB Dor (K1 IV-V), a young active star and XMM/RGS calibration target
The Photon Clean Method algorithm analyzes and outputs models as event lists *** All histograms in this talk are for visualization only
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Spectral : “Perfect” information
Each photon in a simulated observation has ideal (model) wavelength and the wavelength of detection
== “spectral wavelength” from plasma model
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Spectral : “Perfect” informationco
unts
Each photon in a simulated observation has ideal (model) wavelength and the wavelength of detection
== “spectral wavelength” from plasma model
A histogram of the simulated photons’ spectral wavelengths produces sharp lines
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Adding detector response
Photons are stochastically assigned a “detected wavelength”
== “simulated wavelength,” includes redshift, detector and thermal broadening
coun
ts
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Distribution of Model Parameters
Each photon has individual parameter values which may be taken as elements of the parameter distribution
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Distribution of Model Parameters
Each photon has individual parameter values which may be taken as elements of the parameter distribution
The temperature profile of AB Dor is complex; previous fits used 3-temperature or EMD models
coun
ts
Histogram ofPCM solution
Three vertical dashed lines are 3-T XSPEC fit from Sanz-Forcada, Maggio and Micela (2003)
AB Dor Emission Measure Distribution
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
PCM Algorithm Progression
Start: Generate initial model + simulated detected photons from input parameter distribution
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
PCM Algorithm Progression
Start: Generate initial model + simulated detected photons from input parameter distribution
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Photon Generator
For CIE Plasma:• Given a temperature (T), AtomDB generates spectral energy (E).
• Apply ARF test to determine whether photon is detected
• If photon is detected, apply RMF to
determine detected energy (E')
Start: Model Parameter (T)
Result: (T,E,E')+ Ancillary Info
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
PCM Algorithm: Iterate with Feedback
Iteration:• Generate 1 detected photon
Model Esim
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
PCM Algorithm: Iterate with Feedback
Iteration:• Generate 1 detected photon• Replace 1 random photon from model with new photon (E,E',T)
Model Esim
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
PCM Algorithm: Iterate with Feedback
Iteration:• Generate 1 detected photon• Replace 1 random photon from model with new photon (E,E',T)• Compute KS probability statistic
Feedback Test: If KS probability improves with new photon, keep it; Otherwise, throw new photon away and keep old photon
Model Esim
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
PCM Analysis Modes
Phase I: Constrained Convergence
“Re-constrainthe Model”
• Generates a solution which is consistent with a physically realizable model
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
PCM Analysis Modes
Phase II: Un-Constrained Convergence:
• Iterate until KS probability reaches cutoff value, with Monte-Carlo Markov Chain weighting• Photon distribution is not constrained to model probabilities• Allows individual spectral features to be modified to produce best-fit solution
coun
ts
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
PCM Analysis Modes
Phase II: Un-Constrained Convergence:
• Iterate until KS probability reaches cutoff value, with Monte-Carlo Markov Chain weighting• Photon distribution is not constrained to model probabilities• Allows individual spectral features to be modified to produce best-fit solution
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
coun
ts
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Determining Variation in Many-Parameter Models
Low-dimensionality models with few degrees of freedom may be quantified using Chi-square test which has a well-defined error methodology. PCM is appropriate for models of high dimensionality where every photon is a free parameter.
For error determination we use distribution-driven re-sampling methods
Bootstrap Method
coun
ts
PCM solution
XPSEC solution
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Bootstrap Re-Sampling
Method:
1) Randomly resample input data set with substitution to create new data set
2) Perform analysis on new data set to produce new outcome
3) Repeat for n >> 1 re-sampled data sets
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
15.02014.9617.622
17.71121.54916.06214.37613.29812.83317.801
Bootstrap Re-Sampling
Method:
1) Randomly resample input data set with substitution to create new data set
2) Perform analysis on new data set to produce new outcome
3) Repeat for n >> 1 re-sampled data sets
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
15.02014.9617.622
17.71121.54916.06214.37613.29812.83317.801
Bootstrap Re-Sampling
Method:
1) Randomly resample input data set with substitution to create new data set
2) Perform analysis on new data set to produce new outcome
3) Repeat for n >> 1 re-sampled data sets
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
15.0207.6227.622
17.71121.54916.06214.37614.37614.37617.801
15.02014.9617.622
17.71121.54916.06214.37613.29812.83317.801
Bootstrap Re-Sampling
Method:
1) Randomly resample input data set with substitution to create new data set
2) Perform analysis on new data set to produce new outcome
3) Repeat for n >> 1 re-sampled data sets
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Bootstrap Results
AB Dor Emission Measure Distribution
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Bootstrap Results
AB Dor Emission Measure Distribution
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Bootstrap Results
AB Dor Emission Measure Distribution
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Bootstrap Results
AB Dor Emission Measure Distribution
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Bootstrap Results
AB Dor Emission Measure Distribution
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Interpreting the Bootstrap
The variations in the bootstrap solutions estimate errors
The Arithmetic mean of all distributions is plotted as solid line
AB Dor Emission Measure Distribution
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Interpreting the Bootstrap
The variations in the bootstrap solutions estimate errors
The Arithmetic mean of all distributions is plotted as solid line
Confidence levels are computed along vertical axis of distribution
90% confidence
68% confidence
Mean
AB Dor Emission Measure Distribution
X-Ray Spectroscopy WorkshopCambridge, MA Matthew Carpenter, UCB SSL, 7/11/2007
Summary
The Photon Clean Method allows for complicated parameter distributions Phase I solution gives best-fit solution from existing models Phase II solution modifies model to quantify amount of departure from physical models Bootstrap re-sampling may determine variability of trivial and non-trivial solutions without assumptions about the underlying distribution of the data As a test of the PCM’s ability to simultaneously model Fe K and Fe L shell line emission, we are using it to model spectra produced by the LLNL EBIT’s Maxwellian plasma simulator mode.
Thank You